nate stemen

a pal who likes math, physics, and my privacy

Things coming together.


Things feel like they're slowly coming together. Partly because we're getting deep enough into the semester where I'm starting to see overarching themes, and partly because I've had enough free time recently to take some breaks. Most of this semester has been pure Lie theory with some theory of quantum systems peppered in there. That said last week I was working a lot on a paper for that class, and then we have another homework due this upcoming Thursday. It's odd how little we had in the first two months of this class, and now it's getting piled on. That said, I'm not too upset because it's well presented material, super relevant for my research, and a welcome break from only doing Lie theory.

I think my head has been in the weeds with Lie theory this whole semester. What I mean by that is I've been so focused on the details, I haven't been able to find out where we're going. I think the break I've had from constantly doing Lie theory has been helpful to see where we're going.

In Open Quantum Systems we've been getting into some good stuff like the Kraus and Stinespring representation theorems which are both important mathematically and physically. I thought we would get more into some philosophical issues Emerson mentioned in the beginning of the course, but sadly we haven't as much. I'm looking forward to learning more about representations of quantum channels.


I opened the code I wrote for the $\mathsf{SU}(2)$ decomposition problem this week and did a bit of work on it, but haven't figured out where I'm going wrong. I'm meeting with Joel tomorrow to give him a bit of an update on research, but probably mostly just talk about how I've been so busy I haven't been able to spend much time on research. I'd like to discuss with him how I feel overwhelmed and not really that capable of doing research at the moment just because of the workload. I'd also like to suggest we have more regular meetings so I can get more one on one guidance (see the link below about the effectiveness of one on ones). At Overleaf I certainly had a lot more guidance than I do now, and that personally helped a lot. I would like to have a little more of that with Joel as well.


I'm 99% sure I'm buying a car tomorrow. First time in my life, and I'm 26. It's been a great ride not owning one, but it's certainly going to help get me to Waterloo in May. I've been planning that move recently and there is a lot to do. It's coming along slowly.

Oh also baseball started again this week. Baseball was a great distraction from the pandemic last year, and I think it will serve as such again this year.


A light from the end of the semester.


I submitted my Lie theory assignment Wednesday night and pretty much let myself have the rest of the week off, kinda. I didn't do much Lie theory for the class, but my research at the moment is quite Lie theory based, so I have been doing a lot of that. Mostly stuff about Cartan subalgebras and involutions and classifications thereof. Don't understand most of it deeply yet, but I'm enjoying it.

I had a meeting with a colleague Matthew Graydon on Friday, and we made some concrete goals to work on for our project. That was really nice because prior to that I was feeling pretty lost on what I could actually do to contribute to the project because him and Joel advanced the project much more quickly than I was able to keep up. I, of course, don't blame them at all. Research has to get done, and we all want to know the answers. That said, the environment feels more cutthroat than working did. That's maybe partially on me because I don't feel as comfortable asking dumb questions to research colleagues as I did with work colleagues, but overall the environment definitely feels kinda like “get it done or we will”. At the same time, this is the first time anything like this has happened, so I really shouldn't jump to conclusions. I know it's a bad habit of mine, and I really shouldn't attribute malice where there is none.


I've now planned to move to Canada in May, and omg does it feel like there's so much to do before then. From figuring out the car situation, to housing, to taxes and phone plans, I was feeling a bit overwhelmed when I first made my list. As I understand each item better it feels more manageable, and I might have found a car I want to buy, but it's a little too early to tell. There are so many things I did not expect as an international student (that maybe I should've foreseen, but didn't), but the university doesn't seem to be much of a help. At least there are not many resources online. There are immigration consultants, so hopefully they will be able to point me to clearer information than what I see online in other places.

I took myself shopping on Saturday, and between that, and maybe buying a new car, I have a hard time spending money. You can say that's great, but it does inhibit me from enjoying certain aspects of life. I'm not sure where this “fear” of spending money comes from, but it's certainly there. I'm definitely not looking forward to watching my monthly expenses go way up when I move out of my parents place for the first time in a year.

Shits been tiring.


This past week has been a grab bag of emotions. I've definitely felt frustrated a lot this week, but upon reflection not at the sources I pinned it on initially. Doing math remotely right now is in a lot of ways, not fun. I think there are a lot of things that professors can do to make it slightly better, but we're still isolated in a lot of ways. Part of my frustration is at professors for not helping to fill in some of those gaps that can be made up for within the online learning environment. Posting recorded lectures for students to watch on their own means most students never see their classmates faces, and are never in a common space to ask questions and hear other questions from students. A Q&A forum is a good start, but the barrier to write posts is much higher than it is to raise your hand and ask a question in class. I personally do my best not to feel stressed about writing a stupid post, but even the act of writing down a question is more work than raising a hand.

All that said, some of my frustration was because I was/am really struggling with some of the material right now. Last semester was a lot of work, but I never felt like I couldn't understand any of the material. I know that I can, but I'm feeling very slow most of the time. That's a relatively new feeling for me since my struggles in undergrad felt quite different. In particular when I was struggling in undergrad, there is generally so much material you're covering across many different classes, that you just have to do your best for a little while before the class moves on. Now being a graduate student and only taking two courses, I feel a greater priority to really study and understand much more of what's being taught. That's great because I'm almost definitely learning more, but it certainly is more stressful. Moving forward I think I can do a better job of understanding which one of these frustrations I'm feeling and better direct the anger into more meaningful action. The last thing I want to do is lull myself into a state of mind where I think it's not okay to get frustrated at things.

Aside from all that, I'm generally really enjoying the material we're covering. Lie groups/algebras, and representation theory is awesome. I wished I learned some of this stuff in undergrad.


Pushing along S3 cleanup stuff. We're getting close to the end. It seems. My promotion was announced to the team along with two other teammates. That definitely gave me some good feeling recognition which was nice. Still haven't heard anything about my raise though which is somewhat concerning.


I realized that in only having School and Work section on these weekly updates it may seem like those are the only important things in my life. The certainly are not, far from it. There are some privacy concerns about writing about other things online, that I haven't fully thought about, and so I'm just being hesitant. I'm not sure when I'll think about this more, but I don't necessarily have anything against putting some more personal things in here as well. Just wanted to make clear that I don't only care about school and work.


Literally no idea what happened last week.


I finished my Lie theory homework and am not much less confused about how roots and weights work. I'm still working through some of the basics. It's getting better, but only slowly, and new material is coming fast. Kevin said to me today being a math grad student is about “learning how to do math, not understand it” and that feels very accurate. I have no time to understand it!

I've also submitted a final project idea for OQS about unitary $t$-designs and twirling. I've only just started thinking about the project, but expect to hear more later.


We had a hackathon! I did one thing, but kinda two:

  • learned some Rust
  • started working on a zine in $\LaTeX$

Rust was sweet because I've never really learned a typed language, and even though we were doing hello world type exercises in the language, it was really fun thinking about, and being explicit with types. Not only that, but also the Rust compiler is able to catch many types of bugs before code ever leaves your machine! Really cool, and I'd definitely like to learn more.

I know at Quantum Benchmark (the startup my advisor Joel co-started) they use C++, and I've often seen Rust advertised as a safer and easier, and more fun version of C++. So there might be some learning I get to do there. not sure.

As for the zine, I did two things. I took an example LianTze Lim wrote a while back for pocketmods and turned it into a slightly user friendly version. I'm now using that user friendly version to write a “common $\LaTeX$ mistakes in math” zine that I will put on my website, and maybe distribute at conferences and such if those ever happen in person again. It's been fun making, and I hope to one day make it a class file and put it on CTAN. I mostly want to make zine creation more accessible for people who use $\TeX$ as their main means of communication.


Comparatively mild week.


I really didn't want to get behind on my Lie theory homework again so I made sure to start early and I'm making slow progress, but progress. We've been covering representation theory which I've been wanting to learn for a really long time. It's really fascinating to learn about, and understand some of the things I've seen but never had time to really dive into. I'm struggling to understand some of the motivations, and more recently struggling to understand wtf weights and roots are, but hopefully that will come. I'm trying to look at a few different sources to help with all of these problems. Since our professor isn't touching on any of the physics I'm reading some of these notes from 't Hooft and occasionally some of this book by Woit. Both have been helpful getting some insight into how these ideas are used in physics, but I'm definitely still at the “spinning in circles, not quite sure where I am phase”.

The Open Quantum Systems class has only had one lecture in the past 1.5 weeks and no new homework. It feels like I'm taking one class this semester, but I'm not complaining because that one class feels like a lot.

My research was going well, but I think a touch too slow for my advisor and so he made some progress on the problem and sent me and another teammate/colleague some notes on a possible solution. In the notes he's using tools from Lie theory that I haven't really learned yet so I'm trying to understand things about Cartan subalgebras and KAK decompositions to understand the work. I put on hold the numerical work to start studying some of this stuff. I definitely felt a little defeated when he stepped in and solved the problem because I was having fun with it and getting to work on it with Matthew often. I'll probably voice that feeling to Joel at some point, but I also understand it's been multiple months since he suggested this problem and I didn't even work on it for the first few. That said, I've come a long way in understanding the problem since he gave it to me and I should be proud of that and all that I've learned.


Again, cleaning up things on S3, and not much else.


This week was a fucking doozy.


I had assignments for Open Quantum Systems (OQS) and Lie Theory due on wednesday night which led to a stressful first half of the week. The OQS homework wasn't too bad and I had done much of it already, but left two hard questions for the last day. The Lie theory homework was just forever long and I was constantly working on it up until 2 hours before it was due when I couldn't anymore. After submitting both homeworks I needed a break and went for a long walk where I ranted to a friend about my struggles and stressed.

This semester I'm definitely struggling with some material which is leading to some frustration towards myself. Some of that frustration is at prof's who seemingly don't care about students, but I'd be lying if I said it all was. You see last semester, even though I took 3 classes, they were all in subjects I'd seen some of before. It was a great transition to being a student again, but I wasn't particularly challenged by the material (except for quantum info.). But this semester it's totally different and everything I'm learning is challenging. I'm feeling a little bit like the expectations in Lie theory are too high (prof even admitted some of the problems are more involved than he intended, and the assignments are long), but again I'm still figuring out the level of struggle that works best with me.

I'm trying my best to make sure the frustration with myself not solving problems doesn't translate into frustration with classes, but I'm not perfect.

We also had our first meeting for the Equity, Diversity and Inclusion committee. It seems like the first meeting was primarily a formality. Hopefully we talk about real things next time. I also went to a talk about “why women leave (physics)”, and on saturday I attended the Diversity in Quantum Computing Conference. Both were really great, although I really dislike weekend conferences. I think I'll have some new/refreshed ideas to bring to our next EDI meeting.


Deleting more data. I also had my annual review and got a promotion from Associate Engineer to Engineer. Normally that would come with a pay raise, but because of this year it may only be very minimal.


Simultaneously busy and relaxed week.


Technically we were on “reading week” this week. I think that normally would mean there are no lectures, but you probably still have all your normal workload? I'm not totally sure, but the “no lectures” thing wasn't even respected which was a little frustrating. It was in Lie theory, but not open quantum systems (OQS). Perhaps since there were so many technical difficulties at the beginning of the course, the prof felt like he needed to make up, but that seems like something he should bare, not the students.

I spent some time watching the lectures for OQS, and starting the homework for that class as well. The questions I've done have been pretty simple, but proving operators to be positive semi-definite really tripped me up. So much so to the point where I even asked a question on physics.SE which I haven't done in ages. It's really simple in hindsight, but I was computing traces incorrectly for a while. I even sent some of my partial homework write ups to Kevin (math PhD student at Boston College) and he reminded me how crazy physicists are for both not specifying sum limits, and playing with objects with 4 indices. It's a good reminder that even in some areas of math, that would be way too complex. Funny how that works.

I also made some progress on my Lie theory homework, and thankfully the prof put some questions on this homework that are actually quite simple. At least I hope so. It's making me realize the importance of simple questions as means of confidence boosters. The past two assignments have me struggling on almost every question, and it feels nice not to have that here. Solving a problem without resorting to asking around is really rewarding.


I worked quite on this $\mathsf{SU}(2)$ problem, and did some writing about and some coding. I'll be sharing the notes I'm writing internally for some feedback soon. Hopefully I don't write too many basic things for them. Either way it's really helped me understand the problem so that's great.

Also been fun coding in python again. I'm using sympy which I've never used before and good ole numpy which I like, but haven't used in a while.


Pretty slow week work wise, but it was welcomed to go along with my reading week. I have my annual review tomorrow so did some prepping for that, and in the meantime just kept chugging along with deleting data.


I'd like to start trying to write more frequently, and maybe if I commit to writing weekly that will help me.


The beginning of week was mostly spent working on my Lie groups/algebras homework. That class has been super interesting so far, but a few things have been bothering me.

  1. the prof gives way too much homework
  2. the class is going a bit too fast, especially for how much homework is being given
  3. only posting pre-recorded lectures feels lazy to me

I'll explain a bit more what I mean by the last point. When classes were in person (oh so long ago), being in the same place physically gave students a way to have low effort interactions. In my opinion those interactions often lead to things like study groups, casual hangouts, random math chats etc. In an online environment it's surely harder to mimic that, but it's not impossible. By only posting pre-recorded lectures, and then dipping out you're doing the bare minimum in “education”, but you're not providing a space for students to learn. That to me has been really frustrating this week because both my classes are this way.

To make up for the lack of math chats in my life I've gone to a lot of office hours, and formed a small study group in one of my classes, but I'm mostly saddened by the fact Prof's aren't taking more responsibility here. I could go on and explain why I think this is the case, but I'll save that for another time.

After that Lie groups/algebras HW was due wednesday, I transitioned to Open Quantum Systems where I haven't done much for the course. I'm really looking forward to getting more into it, but we haven't actually had that much to do!

I've also been doing a bit of research work on this $\mathsf{SU}(2)$ decomposition problem that Joel gave me. I haven't made much concrete progress on a solution, but I've learned a whole lot while figuring out what the problem even is. I think I have a good grasp on it now, but not sure I have much direction to figure out where to go. Thankfully I'll be chatting with Joel and Matthew next week for some guidance.


Still chugging along on some data removal and S3 cleanup tasks. It's quite fun at this point because it feels like digital landscaping. Or purging. Like running rm -rf on a big folder. Pretty satisfying watching (unecessary) data go down the drain.


I've finished my first semester of graduate school at the University of Waterloo where I study quantum computation. It's been a ride; let me tell you about it.

A little background

Prior to August 2020, I was a full time software developer at Overleaf, and before that I did my bachelors at NYU in mathematics and physics. After 2.5 (lovely) years as a developer I decided it was my time to make graduate school a reality and applied to 15 schools. After a few rejects, and much consideration I decided on U Waterloo for many reasons, but that's for another time. I also decided to continue working for Overleaf part time to help me make a few more bucks, because being a grad student is pretty destitute. Being out of academia for 3 years certainly made me have my doubts if I was going to be able to succeed at school. I had done some data-science work as a developer, but I hadn't really done much of any math, and definitely no quantum mechanics since my undergraduate.

Before starting school I took a month off work to mostly relax and decompress from working, but did also start prepping a little bit for school. Mostly just some elementary reading on quantum computation (I had never formally studied the subject mind you!), and a little refresher of some basic quantum theory. Starting out, I was mainly worried I wouldn't be as good at math as I once was, but I fell quickly into the swing of things.


For my first semester I took three courses:

  • Numerical Analysis
  • Advanced Quantum Theory
  • Introduction to Quantum Information Processing

It seems like most graduate students at U Waterloo take two, but being an international student, the university did not allow me to be a teaching assistant for this semester, so I had a few extra hours per week and thought I could squeeze in an extra course. I chose these three courses for specific reasons:

  • Numerical analysis because of the programming component and that's what I've been doing for the past few years, hence making it not too hard a course
  • Advanced Quantum Theory (which is a cross listed undergrad/grad course where the grad students have an extra project to do at the end) because I hadn't looked at anything quantum for the past 3 years and needed a refresher
  • Quantum Info. Processing because that's the first course in the quantum info track I'm on and it would help me get into research faster

Looking back on the semester, I feel like it was a great selection of courses; it did what I intended, which was help me transition from a working life, to that of a student. Three courses was a bit much, especially on top of working part time (8hrs/week), but it was manageable. I'm certainly looking forward to having a smaller workload in future semesters.

Day to Day Life

Two of my classes (quantum theory, and quantum info) posted recorded lectures on youtube, and in numerical analysis we had live lectures over zoom. All three courses used piazza as a Q&A forum. The youtube lectures were great, but left a lot to be desired in terms of social interaction. I didn't really meet anyone in my quantum theory course, and only managed to meet some friends in quantum info because we set up a study group (shout out Chelsea and Wilson). In numerical analysis the professor had a 15 minute period before class where he encouraged people to “show up and hang out” and chat mostly about non-math stuff, but anything really. As a new student who knew almost no one, I really appreciated it as a way to see some faces and maybe start the process of a friendship.

Most days I would watch one or two lectures, and then primarily work on homework, and oh my god was there a lot. I did a total of 24 problem sets (which you can checkout here:, of which many of the quantum theory ones were pretty tedious. Other than the few tedious calculations I learned a lot from homework, but 3 classes didn't leave me with much time to really dive into anything very deeply (even though I wanted to). That said, this was my first semester and was intended to help get me settled and adjusted. In the future I'll be able to give more time to topics I find interesting.

Overall, working remotely for the past few years prepared me well to get through some of the struggles of online classes (e.g. I really don't have a problem speaking up in online meetings), but learning can be hard when you aren't surrounded by people who are doing the same thing. This was by far the biggest struggle of the semester. Having friends you can talk to about things your learning is so helpful in processing, and digesting material. Big ups to Kevin (also a first year math grad student) who chatted with me a bunch through the semester.

Compared to Work

At the start of the term, I was so happy to be a student again. Life as a student is pretty different from that of a working person; mostly life is much simpler. Problems I faced at work don't often have nice succinct solutions, but rather require analyzing trade-offs and understanding how decisions will affect other arms of the organization. That said, studenthood is much more manicured, and the experience isn't as “disheveled”. Problem sets almost always have “correct” answers, and professors lead you along from one topic to the next. Life is a lot more decided than it was for me when I was working. This “simplicity” was fun and exciting in the beginning, and still is to some degree, but it becomes tiring too. The lack of autonomy can sometimes be a drag, but I remind myself I only have to do 8 courses (3 of which are now done!) before I get to focus on research and have more autonomy there.

The biggest suck about school life is by far the exams. Working was very rarely stressful for me, but exams are stress multipliers. I don't think grading is ever very accurate, but exams must be worse than everything else. Taking an exam for the first time in 3 years wasn't a fun experience and brought back all the memories we drop when we nostalgize about being a student.

Life Outside

Since grad school has been on my to do list for a long time, I definitely poured myself into it fully this semester. That said I also tried to recognize the importance of doing non-school things and taking breaks from work. I definitely don't feel burnt out, but I could do slightly better at this next semester. Here are some highlights from non-school life:

  • read a non-fiction book
  • read some poetry
  • wrote some poetry
  • got outside a good amount in the beginning of the semester
  • cooked a lot of yummy food
  • saw my family (and a few friends) (yes, safely)
  • listened to a lot of good music

Some things I could do better with moving forward are

  • getting outside and getting exercise regularly (god I miss rock climbing with my friends)
  • spending more time with my partner, preferably without a homework assignment in hand
  • spending less time in front of the computer
  • I'm sure many more, but I'll focus on these for now.

It's been a crazy year. Head over to to see some pictures I put together to commemorate making it partway through a pandemic.